Characterize transitions in the black-hole distribution

Characterize the transition mechanisms that connect black-hole distribution-function states at different cosmic times and masses.

Background

The proposed formalism represents black-hole evolution through transition currents between macrostates, such as mass bins at different cosmic epochs. These currents encode the aggregate effects of formation, accretion, mergers, and other stochastic processes.

The paper states that the transitions between distribution-function states are not currently known. Inferring them is necessary for determining the Kramers–Moyal coefficients and for connecting the macroscopic distribution-function evolution to the underlying physical mechanisms.

References

At present, these transitions are unknown from one point of cosmic time to another in the distribution function $\rho_{m, \tau}$.

— Bridging Between Statistical Mechanics and Black Hole Evolution: Theoretical Formalism  (2609.16534 - Mukherjee, 15 Sep 2026) in Section 2, Motivation

Whether the BH mass distribution evolves with redshift, however, remains an open question.

— Probing the Mass--Redshift Dependence of Binary Black Holes and its Implications for $H_0$ with GWTC-5.0  (2609.25662 - Liu et al., 22 Sep 2026) in Abstract